I managed to find a solution. All I do is instead of running the RuneMate.jar file inside the Application's Package Contents I just run the .jar by double clicking it. This works perfectly for me.
If you don't know what I mean, performing the following:
Go to your /Applications/ folder or...
I don't see how the fact that we're running 64 bit should be a problem. That is, unless the runemate client has been built specifically for a 32 bit OS. This could be possible if runemate relies on manipulating low level memory...
I'm also having this problem! I tried running the jar from terminal, which works, but is java version 1.9. It worked but I was unable to attach to the Old School Runescape client...